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Introductory Physics Homework Help
Solving for Φ(k) in Quantum Fourier Transform with ψ(x,0)=e^(-λ*absvalue(x))
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[QUOTE="chris2020, post: 4993465, member: 540872"] [h2]Homework Statement [/h2] Assume ψ(x,0)=e^(-λ*absvalue(x)) for x ± infinity, find Φ(k) [h2]Homework Equations[/h2] Φ(k)=1/√(2π)* ∫e[SUP](-λ*absvalue(x))[/SUP]e[SUP](-i*k*x)[/SUP]dx,-inf, inf[/B][h2]The Attempt at a Solution[/h2] , my thought was Convert the absolute value to ± x depending on what of the number line was being integrated.[/B] U=i*k*x du/(i*k)=dx 1/√(2π)*∫e[SUP]-λ*√(u[SUP]2[/SUP]/(i*k)[SUP]2[/SUP])[/SUP]*e[SUP](-u)[/SUP]du,-inf,inf Now fixing abs value 1/((2π)*(i*k))*∫e[SUP]λ/(i*k)*u[/SUP]e[SUP](-u)[/SUP],du,-inf,o the integrand for one half of the number line looks like: E[SUP](u*(λ/(ik)-1)[/SUP] For which i get: after limits are taken for that half of the integral (1/((λ/ik)-1)) Then similar integral for other half Is this the right track or am i totally off? [B] [/B] [/QUOTE]
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Introductory Physics Homework Help
Solving for Φ(k) in Quantum Fourier Transform with ψ(x,0)=e^(-λ*absvalue(x))
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